Interacting electrons in a one-dimensional random array of scatterers - A Quantum Dynamics and Monte-Carlo study

TL;DR

This paper introduces a novel numerical method combining molecular dynamics and Monte Carlo techniques to study the quantum dynamics of interacting electrons in a one-dimensional disordered system, revealing enhanced conductivity due to interactions.

Contribution

A new approach using Wigner representation and integral equations to analyze quantum dynamics of interacting electrons in disordered systems.

Findings

Interaction increases conductivity compared to noninteracting electrons.

The method effectively computes momentum correlations and spatial dispersions.

Results demonstrate the impact of electron interactions on transport properties.

Abstract

The quantum dynamics of an ensemble of interacting electrons in an array of random scatterers is treated using a new numerical approach for the calculation of average values of quantum operators and time correlation functions in the Wigner representation. The Fourier transform of the product of matrix elements of the dynamic propagators obeys an integral Wigner-Liouville-type equation. Initial conditions for this equation are given by the Fourier transform of the Wiener path integral representation of the matrix elements of the propagators at the chosen initial times. This approach combines both molecular dynamics and Monte Carlo methods and computes numerical traces and spectra of the relevant dynamical quantities such as momentum-momentum correlation functions and spatial dispersions. Considering as an application a system with fixed scatterers, the results clearly demonstrate that the many-particle interaction between the electrons leads to an enhancement of the conductivity and spatial dispersion compared to the noninteracting case.